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Chlamydia trachomatis (Ct) is the most reported sexually transmitted infection in the United States with a major cause of infertility and pelvic inflammatory disease among women. Despite decades of screening women for Ct, rates increase among young African Americans (AA). We create and analyze an agent-based network model to understand the spread of Ct. We calibrate the model parameters to agree with survey data showing Ct prevalence of 12% of the women and 10% of the men in the 15-25 year-old AA in New Orleans, Louisiana. Our model accounts for long-term and casual partnerships. The network captures assortative mixing of individuals by preserving the joint-degree distributions observed in the data. We compare the efficiency of intervention strategies of randomly screening men, partner notification, which includes partner treatment, partner screening, and rescreening for infection. We compare the difference between treating partners of an infected person both with and without testing them. We observe that although increased Ct screening, rescreening and treating most of the partners of infected people will reduce the prevalence, these mitigations alone are not sufficient to control the epidemic. The current practice is to treat the partners of an infected individual, without first testing them for infection. The model predicts that if a sufficient number of the partners of all infected people are tested and treated, then there is a threshold condition where the epidemic can be mitigated. This threshold results from the expanded treatment network created by treating the partners of the infected partners of an individual. Although these conclusions can help design future Ct mitigation studies, we caution the reader that these conclusions are for the mathematical model, not the real world, and are contingent on the validity of the model assumptions.